A four-sided polygon has sides that measure 1 cm, 5cm, and 7 cm. (Forth side not given). What is the perimeter?

Multiplying x by any positive number smaller than 1 will result in some smaller value.

For example, if the scale factor is k = 0.5, then we can think of this as the fraction k = 1/2. Multiplying by 1/2 will make any number smaller, namely, exactly half as much.

We are taking a fractional part of the original number, so its expected the result is smaller. It's like having a whole cake and we only take slices of that cake to end up with the new value. There's no way having one or more slice be larger than the original whole amount.

Because things are getting smaller, we call this type of dilation to be a reduction or we can call it shrinking. This is in contrast to an enlargement when k > 1.

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Claim:  For some positive number k such that k < 1, we have xk < x when x is positive.

The proof of this claim is fairly straight forward.

We multiply both sides of k < 1 by x to get

k < 1

x*k < x*1

xk < x

The inequality sign does not flip because we're multiplying both sides by a positive number x.

So because xk < x, this shows that the original value x gets smaller to xk when we apply the positive scale factor k such that k < 1. This is the same as saying 0 < k < 1. Furthermore, xk < x is the same as 0 < xk < x.

SOLUTION:

Step 1:

In this question, we are given the following:

Applying the root test to the series ∑n=1[infinity]an, where an=(5n−8)2n(3n 4)2n, reveals that the series converges.

To determine the convergence of the series using the root test, we need to consider the limit of the absolute value of the nth root of the general term, as n approaches infinity. In this case, the general term is an=(5n−8)2n(3n 4)2n. Taking the nth root and absolute value, we have:

lim┬(n→∞)⁡〖|an|^(1/n) 〗= lim┬(n→∞)⁡〖|(5n−8)^(2n(3n 4)2n) 〗^(1/n) 〗

Simplifying the expression inside the limit:

|(5n−8)^(2n(3n 4)2n) 〗^(1/n) = |5n−8|^(2(3n 4)) = (5n−8)^(6n-8)

Now, as n approaches infinity, the base (5n−8) grows infinitely large, and since the exponent (6n-8) is also positive, the limit of the expression becomes infinity.

Therefore, lim┬(n→∞)⁡〖|an|^(1/n) 〗= ∞.

Since the limit is greater than 1, according to the root test, the series ∑n=1[infinity]an diverges.

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The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

To find the area between the curves, we need to determine the points of intersection and integrate the difference between the two functions over that interval.

To find the area between the curves y = 8/(1 + x^4) and y = 4x^2, we can plot the curves and calculate the definite integral of the positive difference between the two functions over the interval where they intersect. Here's how you can use a graphing calculator to visualize and calculate the area:

Turn on the graphing calculator and enter the equations of the curves:

For the first curve y = 8/(1 + x^4)

For the second curve, y = 4x^2

Adjust the appropriate window settings on the calculator to ensure that the region of interest is visible. You can set the x-axis range to span the intersection of two curves.

Graph the equations to see the area between the curves.

Determine the values ​​of x where the curves intersect. These are the x values ​​where the two equations have the same y values. You can use the intersection function of the calculator to find these points.

Once you have the intersections, calculate the definite integral of the positive difference between the two curves in the interval where they intersect. This integral will give you the area between the curves.

Alternatively, if you cannot use a graphing calculator or prefer to calculate the area by hand, you can proceed as follows:

Construct an equation to find the points of intersection:

8/(1 + x^4) = 4x^2

Solve the equation to find the values ​​of x where the curves intersect.

Once you have the intersections, set up an integral to find the area between the curves:

A = ∫[a, b] (8/(1 + x^4) - 4x^2) dx

Here [a, b] represents the interval where the curves intersect.

Calculate the definite integral using appropriate integration techniques or software.

The result of the integral will give you the area between the curves.

The area between the curves y = 8/(1 + x⁴) and y = 4x² is approximately 6.193 square units.

Please note that the above steps provide a general guideline for finding the area between two curves. The actual calculations and values ​​will depend on the specific intercepts and integration limits you get from solving graphs or equations.

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Answer:

4.41

Step-by-step explanation:

3.7/(cos(33))=4.411744183

I don't know how many numbers you need

Answer:

-0.333333333333

Step-by-step explanation:

Answer:

This will be as a decimal: 0.33333333333

Step-by-step explanation:

0.4 = 2/5. 0.33333333333… =1/3. 0.237 = 237/1000.

Step-by-step explanation:

Braziliannngffcghjhhb

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The percentile rank / score in the setting of statistics denotes the percentage of the population that falls below it when the data is organized in ascending order.

For the given question.

The difference in the percentiles and raw scores is-

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A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.

To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly payment

P = Principal amount

r = Monthly interest rate

n = Number of monthly payments

In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).

First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.

Next, we substitute the values into the formula:

M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)

Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.

To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.

Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.

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Using a ruler and compasses, draw PQ (7.5cm), locate R using a 6.1cm radius from P, then connect PR. To measure ∠PQR, use a protractor with Q as the center.

To construct triangle PQR with sides PQ = 7.5 cm, QR = 6.1 cm, and ∠PQR = 45 degrees, follow these steps:

1. Draw a line segment PQ of length 7.5 cm using a ruler.

2. Place the compass at point P and draw an arc with a radius of 6.1 cm to intersect PQ. Label this point of intersection as R.

3. Set the compass to a radius of 7.5 cm and draw an arc with center Q.

4. Without changing the compass width, draw another arc with center R to intersect the previous arc. Label this point of intersection as P.

5. Connect points P and Q with a straight line segment to complete triangle PQR.

6. To measure the angle ∠PQR, use a protractor and place it on line segment QR such that the center of the protractor aligns with point Q. Then measure a 45-degree angle starting from the line segment QR and mark the point of intersection on line segment PQ. Label this point as S.

7. Connect points P and S to form the line segment PS.

8. Measure the length of line segment PS using a ruler.

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Answer:

(っ◔◡◔)っ ♥ hi ♥(っ◔◡◔)っ ♥ hi ♥(っ◔◡◔)っ ♥ hi ♥(っ◔◡◔)っ ♥ hi ♥

Step-by-step explanation:

"My wife is really mad at the fact that I have no sense of direction. So I packed up my stuff and right!"

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The required value is 27/8, which is determined when we compute the expression (8-5) ÷ 2 raised to the third power. Thus, the option (C) is correct.

To find the equivalent expression to (8-5) ÷ 2 raised to the third power, we first simplify the expression inside the parentheses:

(8-5) ÷ 2 = 3 ÷ 2.

Next, we raise this simplified expression to the third power:

(3 ÷ 2)³

To evaluate this, we cube both the numerator and denominator:

(3^3) ÷ (2³) = 27 ÷ 8.

Therefore, the expression (8-5) ÷ 2 to the third power is equivalent to 27/8.

Hence, the correct answer is option C: 27/8.

This means that 27/8 is the value we get when we compute the expression (8-5) ÷ 2 raised to the third power.

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Answer:

  14400 cm³/s

Step-by-step explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

  V = s³ . . . . volume in terms of edge length (s)

  dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

  dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s

Answer:

a 48 because it is a multiple of 12

Step-by-step explanation:

Answer:

A 48in

Step-by-step explanation:

the answer is A

hope this helped

In a wheel game with eight equally spaced sectors, Keisha's chances of winning a reward on both spins are 1/16.

Probability—the possibility that an occurrence will happen—is calculated by dividing here the same number of favorable outcomes by the total number of possible outcomes. A coin toss serves as the most simple instance. If you flip a coin, there are only two possible outcomes: heads or tails.

The spinners will get a reward each everytime she lands on white. She will spin the wheel twice.

Here, there are two instances of such color white in the wheel, and there are a total of eight sectors. the likelihood that white will appear in the spin for the first time is,

P = 2/8

P = 1/4

The second case's circumstances are the same. In this instance, the outcomes including both wheel revolutions are independent of one another.

According to the product rule, the likelihood that a white sector will both spin and emerge is,

P = 1/4 * 1/4

P = 1/16

In a wheel game with eight equally spaced sectors, Keisha has a 1/16 chance of winning a reward on both spins.

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The complete question is-

Keisha is playing a game using a wheel divided into eight equal sectors, as shown in the diagram. Each time the spinner lands on white, she will win a prize. If she spins this wheel twice, what is the probability she will win a prize on both spins? Please show all steps!

Using permutation & combination, we can find the following:

a. The permutations of S are: 120.

b. The 3 combinations of S are: 10.

A permutation is an arrangement of several items taken one at a time or all at once in a specific order.

Combinations are based entirely on grouping. Combinations can be used to determine how many different groups that can be created from the available items.

Here in the question,

Given, S = 1; 2; 3; 4; 5

a.

The permutations of S are:

5!

= 5 × 4 × 3 × 2 × 1

= 120

b.

The 3 combinations of S are:

C (n,r)

= C (5,3)

= 5! / [3! × (5-3)!]

= 10.

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Answer:

75

Step-by-step explanation:

it will take 3 week for 3×25 and 5 week for 5×15. I hope this helps.

Answer:

An equation in the form y = mx + b is in the 'slope y-intercept' form where m is the slope and b is the y-intercept. We can rewrite our equation, y = 4, in slope y-intercept form as follows: y = 0x + 4. Here, it is clear that the slope, or m, is zero. Therefore, the slope of the horizontal line y = 4 is zero

The 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

Part I:
The slope of the least-squares regression line is 0.092498, which is option b.

Part II:
To find the confidence interval for the slope β, we use the formula:
β ± t* (s/√n)
where t is the t-value for a 90% confidence interval with (n-2) degrees of freedom, s is the standard error of the estimate, and n is the sample size.
From the output, we have s = 466.2 and n = 19.
To find the t-value, we can use a t-distribution table or a calculator. For a 90% confidence interval with 17 degrees of freedom, the t-value is approximately 1.734.
Substituting the values, we get:
0.092498 ± 1.734 * (466.2/√19)
Simplifying, we get:
0.092498 ± 0.099
Therefore, the 90% confidence interval for the slope β is approximately (0.079 to 0.106), which is option b.

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Answer:

YES HE CAN

Step-by-step explanation:

Answer:

when you have Bob anything is possible

Step-by-step explanation:

I don't see any numbers, so I just give you an example :

11

every position in a number is worth 10 times the value of the position to its very right.

so, in e.g. 11

the left 1 is worth 10 times the value of the right 1.

Answer:

  (a)  (-1, 2)

Step-by-step explanation:

You want the ordered pair that represents the coordinates of a point 1 unit left and 2 units up from the origin.

The (x, y) coordinates of a point on the Cartesian plane represent (units right, units up) relative to the origin. When the direction is left or down, the sign of the corresponding coordinate is made negative.

  (1 left, 2 up)   ⇒   (-1, 2), matching choice A

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Answer:

which ones do you need help with?

Answer:

x < -5

Step-by-step explanation:

For the most part, you solve inequalities the same way you solve equations. So for this one, we just needed to divide both sides by 2.

The solution to the inequality is: x < -5. To solve the inequality 2x < -10, follow these steps:

1. Divide both sides of the inequality by 2 to isolate x.

2. Remember to reverse the inequality sign when dividing by a negative number.

Step 1: Divide both sides by 2:

(2x) / 2 < (-10) / 2

Step 2: Simplify:

x < -5

The solution to the inequality is:

x < -5

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Answer: 8.4261

Step-by-step explanation:

On factoring the angles ∠2 = 5x - 28 and ∠4 = 3x - 10, the value for ∠3 in a parallelogram is obtained as 163°.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

In a parallelogram, opposite angles are congruent, so we have -

∠2 = ∠4

5x - 28 = 3x - 10

Solving for x, we get -

2x = 18

x = 9

Now that we know the value of x, we can find the measure of ∠3.

In a parallelogram, adjacent angles are supplementary, so we have -

angle 2 + angle 3 = 180°

Substituting the values of ∠2 and x, we get -

5x - 28 + ∠3 = 180°

5(9) - 28 + ∠3 = 180°

45 - 28 + ∠3 = 180°

17 + ∠3 = 180°

Solving for ∠3, we get -

∠3 = 180 - 17

∠3 = 163°

Therefore, the measure of ∠3 is 163°.

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Time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

According to the question we have been given that,

Total time taken by Matilda to complete the consulting projects = \(16\frac{3}{4}\) hours

First we will convert it into simple fraction which is

         \(16\frac{3}{4} = \frac{67}{4} \\\) hours

Number of consulting projects = 3

And Matilda spends same amount of time to each of the project.

To find the time she spend on each project is by using unitary method

that is,            3 projects = \(\frac{67}{4}\) hours

                      1 project = \(\frac{67}{4} / 3\)

                                     = 67/12

                                     = \(5\frac{7}{12}\) hours

Hence time taken by Matilda on each project is \(5\frac{7}{12}\) hours.

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